#############################################################################
##
##  This file is part of GAP, a system for computational discrete algebra.
##  This file's authors include Gábor Horváth, Stefan Kohl.
##
##  Copyright of GAP belongs to its developers, whose names are too numerous
##  to list here. Please refer to the COPYRIGHT file for details.
##
##  SPDX-License-Identifier: GPL-2.0-or-later
##
##  This file contains a list of precomputed structure descriptions of small
##  groups.
##
##  NAMES_OF_SMALL_GROUPS[n][i] is the description corresponding to
##  SmallGroup(n,i).
##

NAMES_OF_SMALL_GROUPS :=
[ [ "1" ],
 [ "C2" ],
 [ "C3" ],
 [ "C4",
 "C2 x C2" ],
 [ "C5" ],
 [ "S3",
 "C6" ],
 [ "C7" ],
 [ "C8",
 "C4 x C2",
 "D8",
 "Q8",
 "C2 x C2 x C2" ],
 [ "C9",
 "C3 x C3" ],
 [ "D10",
 "C10" ],
 [ "C11" ],
 [ "C3 : C4",
 "C12",
 "A4",
 "D12",
 "C6 x C2" ],
 [ "C13" ],
 [ "D14",
 "C14" ],
 [ "C15" ],
 [ "C16",
 "C4 x C4",
 "(C4 x C2) : C2",
 "C4 : C4",
 "C8 x C2",
 "C8 : C2",
 "D16",
 "QD16",
 "Q16",
 "C4 x C2 x C2",
 "C2 x D8",
 "C2 x Q8",
 "(C4 x C2) : C2",
 "C2 x C2 x C2 x C2" ],
 [ "C17" ],
 [ "D18",
 "C18",
 "C3 x S3",
 "(C3 x C3) : C2",
 "C6 x C3" ],
 [ "C19" ],
 [ "C5 : C4",
 "C20",
 "C5 : C4",
 "D20",
 "C10 x C2" ],
 [ "C7 : C3",
 "C21" ],
 [ "D22",
 "C22" ],
 [ "C23" ],
 [ "C3 : C8",
 "C24",
 "SL(2,3)",
 "C3 : Q8",
 "C4 x S3",
 "D24",
 "C2 x (C3 : C4)",
 "(C6 x C2) : C2",
 "C12 x C2",
 "C3 x D8",
 "C3 x Q8",
 "S4",
 "C2 x A4",
 "C2 x C2 x S3",
 "C6 x C2 x C2" ],
 [ "C25",
 "C5 x C5" ],
 [ "D26",
 "C26" ],
 [ "C27",
 "C9 x C3",
 "(C3 x C3) : C3",
 "C9 : C3",
 "C3 x C3 x C3" ],
 [ "C7 : C4",
 "C28",
 "D28",
 "C14 x C2" ],
 [ "C29" ],
 [ "C5 x S3",
 "C3 x D10",
 "D30",
 "C30" ],
 [ "C31" ],
 [ "C32",
 "(C4 x C2) : C4",
 "C8 x C4",
 "C8 : C4",
 "(C8 x C2) : C2",
 "(C2 x C2 x C2) : C4",
 "(C8 : C2) : C2",
 "C2 . ((C4 x C2) : C2) = (C2 x C2) . (C4 x C2)",
 "(C8 x C2) : C2",
 "Q8 : C4",
 "(C4 x C4) : C2",
 "C4 : C8",
 "C8 : C4",
 "C8 : C4",
 "C4 . D8 = C4 . (C4 x C2)",
 "C16 x C2",
 "C16 : C2",
 "D32",
 "QD32",
 "Q32",
 "C4 x C4 x C2",
 "C2 x ((C4 x C2) : C2)",
 "C2 x (C4 : C4)",
 "(C4 x C4) : C2",
 "C4 x D8",
 "C4 x Q8",
 "(C2 x C2 x C2 x C2) : C2",
 "(C4 x C2 x C2) : C2",
 "(C2 x Q8) : C2",
 "(C4 x C2 x C2) : C2",
 "(C4 x C4) : C2",
 "(C2 x C2) . (C2 x C2 x C2)",
 "(C4 x C4) : C2",
 "(C4 x C4) : C2",
 "C4 : Q8",
 "C8 x C2 x C2",
 "C2 x (C8 : C2)",
 "(C8 x C2) : C2",
 "C2 x D16",
 "C2 x QD16",
 "C2 x Q16",
 "(C8 x C2) : C2",
 "C8 : (C2 x C2)",
 "(C2 x Q8) : C2",
 "C4 x C2 x C2 x C2",
 "C2 x C2 x D8",
 "C2 x C2 x Q8",
 "C2 x ((C4 x C2) : C2)",
 "(C2 x C2 x C2) : (C2 x C2)",
 "(C2 x Q8) : C2",
 "C2 x C2 x C2 x C2 x C2" ],
 [ "C33" ],
 [ "D34",
 "C34" ],
 [ "C35" ],
 [ "C9 : C4",
 "C36",
 "(C2 x C2) : C9",
 "D36",
 "C18 x C2",
 "C3 x (C3 : C4)",
 "(C3 x C3) : C4",
 "C12 x C3",
 "(C3 x C3) : C4",
 "S3 x S3",
 "C3 x A4",
 "C6 x S3",
 "C2 x ((C3 x C3) : C2)",
 "C6 x C6" ],
 [ "C37" ],
 [ "D38",
 "C38" ],
 [ "C13 : C3",
 "C39" ],
 [ "C5 : C8",
 "C40",
 "C5 : C8",
 "C5 : Q8",
 "C4 x D10",
 "D40",
 "C2 x (C5 : C4)",
 "(C10 x C2) : C2",
 "C20 x C2",
 "C5 x D8",
 "C5 x Q8",
 "C2 x (C5 : C4)",
 "C2 x C2 x D10",
 "C10 x C2 x C2" ],
 [ "C41" ],
 [ "C7 : C6",
 "C2 x (C7 : C3)",
 "C7 x S3",
 "C3 x D14",
 "D42",
 "C42" ],
 [ "C43" ],
 [ "C11 : C4",
 "C44",
 "D44",
 "C22 x C2" ],
 [ "C45",
 "C15 x C3" ],
 [ "D46",
 "C46" ],
 [ "C47" ],
 [ "C3 : C16",
 "C48",
 "(C4 x C4) : C3",
 "C8 x S3",
 "C24 : C2",
 "C24 : C2",
 "D48",
 "C3 : Q16",
 "C2 x (C3 : C8)",
 "(C3 : C8) : C2",
 "C4 x (C3 : C4)",
 "(C3 : C4) : C4",
 "C12 : C4",
 "(C12 x C2) : C2",
 "(C3 x D8) : C2",
 "(C3 : Q8) : C2",
 "(C3 x Q8) : C2",
 "C3 : Q16",
 "(C6 x C2) : C4",
 "C12 x C4",
 "C3 x ((C4 x C2) : C2)",
 "C3 x (C4 : C4)",
 "C24 x C2",
 "C3 x (C8 : C2)",
 "C3 x D16",
 "C3 x QD16",
 "C3 x Q16",
 "C2 . S4 = SL(2,3) . C2",
 "GL(2,3)",
 "A4 : C4",
 "C4 x A4",
 "C2 x SL(2,3)",
 "((C4 x C2) : C2) : C3",
 "C2 x (C3 : Q8)",
 "C2 x C4 x S3",
 "C2 x D24",
 "(C12 x C2) : C2",
 "D8 x S3",
 "(C4 x S3) : C2",
 "Q8 x S3",
 "(C4 x S3) : C2",
 "C2 x C2 x (C3 : C4)",
 "C2 x ((C6 x C2) : C2)",
 "C12 x C2 x C2",
 "C6 x D8",
 "C6 x Q8",
 "C3 x ((C4 x C2) : C2)",
 "C2 x S4",
 "C2 x C2 x A4",
 "(C2 x C2 x C2 x C2) : C3",
 "C2 x C2 x C2 x S3",
 "C6 x C2 x C2 x C2" ],
 [ "C49",
 "C7 x C7" ],
 [ "D50",
 "C50",
 "C5 x D10",
 "(C5 x C5) : C2",
 "C10 x C5" ],
 [ "C51" ],
 [ "C13 : C4",
 "C52",
 "C13 : C4",
 "D52",
 "C26 x C2" ],
 [ "C53" ],
 [ "D54",
 "C54",
 "C3 x D18",
 "C9 x S3",
 "(C3 x C3) : C6",
 "C9 : C6",
 "(C9 x C3) : C2",
 "((C3 x C3) : C3) : C2",
 "C18 x C3",
 "C2 x ((C3 x C3) : C3)",
 "C2 x (C9 : C3)",
 "C3 x C3 x S3",
 "C3 x ((C3 x C3) : C2)",
 "(C3 x C3 x C3) : C2",
 "C6 x C3 x C3" ],
 [ "C11 : C5",
 "C55" ],
 [ "C7 : C8",
 "C56",
 "C7 : Q8",
 "C4 x D14",
 "D56",
 "C2 x (C7 : C4)",
 "(C14 x C2) : C2",
 "C28 x C2",
 "C7 x D8",
 "C7 x Q8",
 "(C2 x C2 x C2) : C7",
 "C2 x C2 x D14",
 "C14 x C2 x C2" ],
 [ "C19 : C3",
 "C57" ],
 [ "D58",
 "C58" ],
 [ "C59" ],
 [ "C5 x (C3 : C4)",
 "C3 x (C5 : C4)",
 "C15 : C4",
 "C60",
 "A5",
 "C3 x (C5 : C4)",
 "C15 : C4",
 "S3 x D10",
 "C5 x A4",
 "C6 x D10",
 "C10 x S3",
 "D60",
 "C30 x C2" ],
 [ "C61" ],
 [ "D62",
 "C62" ],
 [ "C7 : C9",
 "C63",
 "C3 x (C7 : C3)",
 "C21 x C3" ],
,
 [ "C65" ],
 [ "C11 x S3",
 "C3 x D22",
 "D66",
 "C66" ],
 [ "C67" ],
 [ "C17 : C4",
 "C68",
 "C17 : C4",
 "D68",
 "C34 x C2" ],
 [ "C69" ],
 [ "C7 x D10",
 "C5 x D14",
 "D70",
 "C70" ],
 [ "C71" ],
 [ "C9 : C8",
 "C72",
 "Q8 : C9",
 "C9 : Q8",
 "C4 x D18",
 "D72",
 "C2 x (C9 : C4)",
 "(C18 x C2) : C2",
 "C36 x C2",
 "C9 x D8",
 "C9 x Q8",
 "C3 x (C3 : C8)",
 "(C3 x C3) : C8",
 "C24 x C3",
 "((C2 x C2) : C9) : C2",
 "C2 x ((C2 x C2) : C9)",
 "C2 x C2 x D18",
 "C18 x C2 x C2",
 "(C3 x C3) : C8",
 "(C3 : C4) x S3",
 "(C3 x C3) : (C4 x C2)",
 "(C6 x S3) : C2",
 "(C6 x S3) : C2",
 "(C3 x C3) : Q8",
 "C3 x SL(2,3)",
 "C3 x (C3 : Q8)",
 "C12 x S3",
 "C3 x D24",
 "C6 x (C3 : C4)",
 "C3 x ((C6 x C2) : C2)",
 "(C3 x C3) : Q8",
 "C4 x ((C3 x C3) : C2)",
 "(C12 x C3) : C2",
 "C2 x ((C3 x C3) : C4)",
 "(C6 x C6) : C2",
 "C12 x C6",
 "C3 x C3 x D8",
 "C3 x C3 x Q8",
 "(C3 x C3) : C8",
 "(S3 x S3) : C2",
 "(C3 x C3) : Q8",
 "C3 x S4",
 "(C3 x A4) : C2",
 "A4 x S3",
 "C2 x ((C3 x C3) : C4)",
 "C2 x S3 x S3",
 "C6 x A4",
 "C2 x C6 x S3",
 "C2 x C2 x ((C3 x C3) : C2)",
 "C6 x C6 x C2" ],
 [ "C73" ],
 [ "D74",
 "C74" ],
 [ "C75",
 "(C5 x C5) : C3",
 "C15 x C5" ],
 [ "C19 : C4",
 "C76",
 "D76",
 "C38 x C2" ],
 [ "C77" ],
 [ "C13 : C6",
 "C2 x (C13 : C3)",
 "C13 x S3",
 "C3 x D26",
 "D78",
 "C78" ],
 [ "C79" ],
 [ "C5 : C16",
 "C80",
 "C5 : C16",
 "C8 x D10",
 "C40 : C2",
 "C40 : C2",
 "D80",
 "C5 : Q16",
 "C2 x (C5 : C8)",
 "(C5 : C8) : C2",
 "C4 x (C5 : C4)",
 "(C5 : C4) : C4",
 "C20 : C4",
 "(C20 x C2) : C2",
 "(C5 x D8) : C2",
 "(C5 : Q8) : C2",
 "(C5 x Q8) : C2",
 "C5 : Q16",
 "(C10 x C2) : C4",
 "C20 x C4",
 "C5 x ((C4 x C2) : C2)",
 "C5 x (C4 : C4)",
 "C40 x C2",
 "C5 x (C8 : C2)",
 "C5 x D16",
 "C5 x QD16",
 "C5 x Q16",
 "C5 : (C8 x C2)",
 "(C5 : C8) : C2",
 "C4 x (C5 : C4)",
 "C20 : C4",
 "C2 x (C5 : C8)",
 "(C5 : C8) : C2",
 "(C10 x C2) : C4",
 "C2 x (C5 : Q8)",
 "C2 x C4 x D10",
 "C2 x D40",
 "(C20 x C2) : C2",
 "D8 x D10",
 "(C4 x D10) : C2",
 "Q8 x D10",
 "(C4 x D10) : C2",
 "C2 x C2 x (C5 : C4)",
 "C2 x ((C10 x C2) : C2)",
 "C20 x C2 x C2",
 "C10 x D8",
 "C10 x Q8",
 "C5 x ((C4 x C2) : C2)",
 "(C2 x C2 x C2 x C2) : C5",
 "C2 x C2 x (C5 : C4)",
 "C2 x C2 x C2 x D10",
 "C10 x C2 x C2 x C2" ],
 [ "C81",
 "C9 x C9",
 "(C9 x C3) : C3",
 "C9 : C9",
 "C27 x C3",
 "C27 : C3",
 "(C3 x C3 x C3) : C3",
 "(C9 x C3) : C3",
 "(C9 x C3) : C3",
 "C3 . ((C3 x C3) : C3) = (C3 x C3) . (C3 x C3)",
 "C9 x C3 x C3",
 "C3 x ((C3 x C3) : C3)",
 "C3 x (C9 : C3)",
 "(C9 x C3) : C3",
 "C3 x C3 x C3 x C3" ],
 [ "D82",
 "C82" ],
 [ "C83" ],
 [ "C7 : C12",
 "C4 x (C7 : C3)",
 "C7 x (C3 : C4)",
 "C3 x (C7 : C4)",
 "C21 : C4",
 "C84",
 "C2 x (C7 : C6)",
 "S3 x D14",
 "C2 x C2 x (C7 : C3)",
 "C7 x A4",
 "(C14 x C2) : C3",
 "C6 x D14",
 "C14 x S3",
 "D84",
 "C42 x C2" ],
 [ "C85" ],
 [ "D86",
 "C86" ],
 [ "C87" ],
 [ "C11 : C8",
 "C88",
 "C11 : Q8",
 "C4 x D22",
 "D88",
 "C2 x (C11 : C4)",
 "(C22 x C2) : C2",
 "C44 x C2",
 "C11 x D8",
 "C11 x Q8",
 "C2 x C2 x D22",
 "C22 x C2 x C2" ],
 [ "C89" ],
 [ "C5 x D18",
 "C9 x D10",
 "D90",
 "C90",
 "C3 x C3 x D10",
 "C15 x S3",
 "C3 x D30",
 "C5 x ((C3 x C3) : C2)",
 "(C15 x C3) : C2",
 "C30 x C3" ],
 [ "C91" ],
 [ "C23 : C4",
 "C92",
 "D92",
 "C46 x C2" ],
 [ "C31 : C3",
 "C93" ],
 [ "D94",
 "C94" ],
 [ "C95" ],
,
 [ "C97" ],
 [ "D98",
 "C98",
 "C7 x D14",
 "(C7 x C7) : C2",
 "C14 x C7" ],
 [ "C99",
 "C33 x C3" ],
 [ "C25 : C4",
 "C100",
 "C25 : C4",
 "D100",
 "C50 x C2",
 "C5 x (C5 : C4)",
 "(C5 x C5) : C4",
 "C20 x C5",
 "C5 x (C5 : C4)",
 "(C5 x C5) : C4",
 "(C5 x C5) : C4",
 "(C5 x C5) : C4",
 "D10 x D10",
 "C10 x D10",
 "C2 x ((C5 x C5) : C2)",
 "C10 x C10" ] ];
MakeReadOnlyGlobal( "NAMES_OF_SMALL_GROUPS" );
